The variance of a data set is the square of its standard deviation. Given the standard deviation of the weights is $12.1126$ kg, we can find the variance by squaring this value:

$\text{Variance} = (\text{Standard Deviation})^2 = (12.1126)^2$

Let's calculate the variance:

$\text{Variance} = 12.1126^2$The variance of the sample data is approximately $146.7151 \, \text{kg}^2$ when rounded to four decimal places.

Would you like further details or have any questions?

Here are some related questions that could expand your understanding:

1. How is variance different from standard deviation?
2. Why is variance expressed in squared units?
3. How would the variance change if the standard deviation were larger or smaller?
4. What are some common uses of variance in statistics?
5. How is variance calculated for a population versus a sample?

Tip: Remember, variance is sensitive to outliers because it squares the deviations, amplifying larger differences from the mean.